Electromagnetic (EM) properties of hydrocarbon-filled and water-filled reservoirs differ significantly. For example, the resistivity difference between the two cases can be up to two orders of magnitude. Electromagnetic methods (EM) exploit these differences to predict the nature of a reservoir and reduce costs in hydrocarbon exploration. Recently, the controlled-source electromagnetic (“CSEM”) method is becoming a promising direct-hydrocarbon-indicator (“DHI”) tool to de-risk drilling decisions; see for example U.S. Pat. No. 6,522,146 to Srnka.
Inversion (or imaging) is fundamental to analyzing CSEM data for hydrocarbon exploration (Carazzone, et al., SEG Expanded Abstract 24, P575 (2005)). Inversion is a procedure for obtaining earth models that are consistent with the measured data. The inversion process thus provides physically meaningful information on both rock properties and earth structure. Inversion methods are typically implemented as an optimization problem in which the mismatch between measured and forward synthesized data is minimized. For CSEM data, forward synthesis or forward modeling uses Maxwell's equations to simulate the earth's response for a given set of model parameters and can be described mathematically by d=F(m), where d is a vector of measured data and m is a model of the earth's resistivity. The operator F thus provides a means to compute d for any given model m. The inverse problem is to find the values m that yield the given data d and may be written symbolically as m=F−1(d). The inverse operator F−1 is nonlinear and non-unique for CSEM inversion. In addition to the mismatch between measured and synthetic data, the inverse problem includes a model regularization term intended to dampen non-physical fluctuations in m. A simple and computationally tractable approach to the nonlinear multi-dimensional inverse problem is iterative linearized inversion. The nonlinear relationship between data and model in the forward problem is approximated by d=F(m0)+Gδm, where the model update, δm, is assumed to be small. The model update δm relative to a previous model m0 is obtained by solving the linear system Gδm=b, where G is the Jacobian matrix and b=d−F(m0) is the data residual. The model can be updated iteratively by adding δm to m0 until a satisfactory fit to the data has been achieved. The inverse problem and its solution have been studied extensively. See, for example, R. L. Parker, Geophysical Inverse Theory, (1994); W. Menke, Geophysical Data Analysis: Discrete Inverse Theory, (1989); and A. Tarantola, Inverse Problem Theory, (1987). These are general background treatises that the skilled practitioner will not need to refer to and which are considered to have no direct bearing on the invention disclosed below.
Inversion of EM data can provide unique information related to reservoir location, shape and fluid properties. However, the model derived from this inversion process is affected not only by the mathematical formulation and implementation of the inverse problem but also by the measurement system and survey design. Sometimes such “artifacts” can appear in inversion results. For example, Zhdanov and Hursan observe that the Born inversion gives a large number of unwanted artifacts while the focusing inversion algorithm obtains much more realistic models (“3D electromagnetic inversion based on quasi-analytic approximation,” Inverse Problems 16, 1297-1322 (2000)). In cross-well EM inversion, Alumbaugh observes that artifacts appear near the bottom of the receiver well. He attributes it to the geology not obeying the cylindrical assumptions employed in his inversion scheme (“Linearized and nonlinear parameter variance estimation for two-dimensional electromagnetic induction inversion,” Inverse Problem 16, 1323-1341 (2000)). In the same paper, Alumbaugh also notices that immediately adjacent to the transmitter well the error estimates are greater than near the center of the borehole region and/or near the receiver well when he is doing error estimation on inversion results. However, one would expect this region to have lower uncertainty estimates as the sensitivity of the data to the model for the cross-well configuration is greatest in the regions near the sources and receivers. He determines this seemingly erroneous behavior is caused by the fact he is coupling the cylindrical geometry with the minimization of the first-derivative constraint. To eliminate this artifact in error estimate, he proposes a method to constrain the model in cells immediately adjacent to the transmitter borehole to known conductivities derived from the well logs by employing very tight bounds. Commer and Newman (“New advances in three-dimensional controlled-source electromagnetic inversion”, Geophysical Journal International 172, 513-535 (2008)) experience artifacts due to statics and positioning errors at the detectors. They call those near-surface image artifacts “source signature.” By following Pratt for seismic waveform inversion, they assign an unknown complex scaling factor to each CSEM source to take into account data distortions in the form of both amplitude and phase shifts. (Pratt, “Seismic waveform inversion in the frequency domain, Part 1: Theory and verification in a physical scale model”, Geophysics 64, 888-901 (1999).
It is well known that the final recovered earth model from the inversion process is not unique. In other words, many models can provide an acceptable fit to the measured data, since the data are finite in number and of limited accuracy. Mathematical approaches such as regularization are often implemented in inversion algorithms to mitigate some aspects of the non-uniqueness problem. A popular approach involves including model regularization terms in the objective function to be minimized, particularly regularization terms that penalize roughness of the model (Tikhonov and Arsenin, Solutions of ill-posed problems, F. John, Translation Editor, V. H. Winston and Sons (distributed by Wiley, New York), (1977); Parker, “The theory of ideal bodies for gravity interpretation,” Geophy. J. R. astr. Soc. 42, 315-334 (1975); Constable et al., “Occam's inversion: a practical algorithm for generating smooth models from EM sounding data,” Geophysics 52, 289-300 (1987); Smith and Booker, “Magnetotelluric inversion for minimum structure,” Geophysics 53, 1565-1576 (1988)). The Tikhonov and Arsenin book is of historical interest because it was the first use of regularization in inversion. Regularization may be useful for mitigating artifacts below the receivers, but it is not designed specifically to suppress the acquisition signature in CSEM inversion results. In fact, the inversion algorithm used to generate the results in FIG. 1 includes a regularization term designed to produce a smooth model; it has clearly not eliminated the artifacts.
The use of strict bounds for cells near borehole may be feasible for cross-well imaging since resistivity logs are available, but not feasible for all cells near receivers in marine CSEM case because resistivities of shallow subsurface over a survey area are normally not known. The so-called “source signature” experienced by Commer and Newman is due to near-surface statics and positioning error, in contrast to the acquisition system signature addressed by the present invention which is intrinsic.
The inventors know of no methods that have been developed specifically for suppressing the acquisition system overprint in CSEM inversion. Such a method is needed, and the present invention fulfills this need to suppress artifacts associated with the acquisition system, thereby making it possible to generate more reliable and geologically consistent resistivity images.